Archives for Basic Quantum Theory - Page 5
2 free non interacting particles and the EPR paradox
EPR Paradox for Two Non-Interacting Particles The EPR paradox (named after Einstein, Podolsky, and Rosen) arises when considering quantum entanglement and the nature of reality. It challenges the completeness of…
Two free non-interacting particles
Two Non Interacting Particles? It is possible to construct a two-particle wave function for non-interacting particles. The total wave function is simply the product of the individual wave functions in…
Free Particle wave function in momentum eigenstates
Free Particle Wave Function The free-particle wave function can be expressed as an integral over momentum space: ψ(x,t) = (1/√(2πħ)) ∫-∞∞ ψ̃(p) ei(px - Et)/ħ dp where ψ̃(p) is the…
Complex fourier transform and Wave Packets
Constructing a wave that is spiked in just one small region is not easy. When you superpose several waves, you have to do so in a way that they constructively…
State of an atom after passing through three Stern Gerlach Analyzers Successively
Two SG Detectors - at 90 degrees to each other. First one (SG oriented along z axis) - exiting atom is +m (z axis) (or -m on the z axis).…
Convolution Integrals for Entangled Quantum States
Convolution Integrals in Schrödinger’s Equation for Entangled Systems 1. Green's Functions and Propagators The solution to the time-dependent Schrödinger equation often involves propagators, which describe the evolution of a wavefunction…
Finite Abelian Groups and Applications to Quantum Physics
Finite Abelian Groups and Applications to Quantum Physics What Are Finite Abelian Groups? A finite abelian group is a group \( G \) with the following properties: Closure: For any…
Trajectories don’t exist
One of Heisenberg's greatest triumphs was simply eliminating the whole thought process around classical electron trajectories. He claimed that there are only observable quantities - and these quantities can be…
Dipole Approximation in Electron-Photon Interaction
Dipole Approximation for Electron-Photon Interaction The dipole approximation assumes that the wavelength of the electromagnetic field is much larger than the spatial extent of the electron wavefunction. In this case,…
Electron interacts with a photon – Schrodinger equation and it’s solution
Schrödinger Equation for Electron-Photon Interaction The system includes: An electron with wavefunction ψe(r, t), A photon field described by the vector potential A(r, t). The total Hamiltonian includes: The electron's…